Tour of regular temperaments: Difference between revisions

Line 125:

===[[Ditonmic family|Ditonmic or Lala-theyo family]] (P8, c<sup>4</sup>P4/13)===

This tempers out the ditonma, {{Monzo|-27 -2 13}} = 1220703125/1207959552. Thirteen ~[-12 -1 6> generators of about 407¢ equals a quadruple-compound 4th. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies ~~53-edo~~, which is a good tuning for this high-accuracy family of temperaments.

This tempers out the ditonma, {{Monzo|-27 -2 13}} = 1220703125/1207959552. Thirteen ~{{Monzo|-12 -1 6}} generators of about 407¢ equals a quadruple-compound 4th. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53EDO, which is a good tuning for this high-accuracy family of temperaments.

===[[Luna family|Luna or Sasa-quintrigu family]] (P8, ccP4/15)===

Line 137:

===[[Maquila family|Maquila or Trisa-segu family]] (P8, c<sup>7</sup>P5/17)===

This tempers out the maquila comma, 562949953421312/556182861328125 = {{Monzo|49 -6 -17}};. The generator is ~512/375 = ~535¢. Seventeen generators equals a septuple-compound 5th. 5/4 is equated to 3 octaves minus 6 generators. An obvious 11-limit interpretation of the generator is 11/8, leading to the Lala-selo temperament. However, Lala-selo isn't nearly as accurate as Trisa-segu.

This tempers out the maquila comma, 562949953421312/556182861328125 = {{Monzo|49 -6 -17}}. The generator is ~512/375 = ~535¢. Seventeen generators equals a septuple-compound 5th. 5/4 is equated to 3 octaves minus 6 generators. An obvious 11-limit interpretation of the generator is 11/8, leading to the Lala-selo temperament. However, Lala-selo isn't nearly as accurate as Trisa-segu.

===[[Gammic family|Gammic or Laquinquadyo family]] (P8, P5/20)===

Line 368:

===[[Hemifamity temperaments|Hemifamity or Saruyo temperaments]]===

Hemifamity rank-two temperaments temper out the hemifamity comma, {{Monzo|10 -6 1 -1}} = 5120/5103.

===[[Parkleiness temperaments|Parkleiness or Zotritrigu temperaments]]===

Parkleiness rank-two temperaments temper out the ''parkleiness'' comma, {{Monzo|7 7 -9 1}} = 1959552/1953125.

===[[Porwell temperaments|Porwell or Sarurutrigu temperaments]]===

@@ Line 125: / Line 125: @@
 ===[[Ditonmic family|Ditonmic or Lala-theyo family]] (P8, c<sup>4</sup>P4/13)===
-This tempers out the ditonma, {{Monzo|-27 -2 13}} = 1220703125/1207959552. Thirteen ~[-12 -1 6> generators of about 407¢ equals a quadruple-compound 4th.  5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53-edo, which is a good tuning for this high-accuracy family of temperaments.
+This tempers out the ditonma, {{Monzo|-27 -2 13}} = 1220703125/1207959552. Thirteen ~{{Monzo|-12 -1 6}} generators of about 407¢ equals a quadruple-compound 4th.  5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53EDO, which is a good tuning for this high-accuracy family of temperaments.
 ===[[Luna family|Luna or Sasa-quintrigu family]] (P8, ccP4/15)===
@@ Line 137: / Line 137: @@
 ===[[Maquila family|Maquila or Trisa-segu family]] (P8, c<sup>7</sup>P5/17)===
-This tempers out the maquila comma, 562949953421312/556182861328125 = {{Monzo|49 -6 -17}};. The generator is ~512/375 = ~535¢. Seventeen generators equals a septuple-compound 5th.  5/4 is equated to 3 octaves minus 6 generators. An obvious 11-limit interpretation of the generator is 11/8, leading to the Lala-selo temperament. However, Lala-selo isn't nearly as accurate as Trisa-segu.
+This tempers out the maquila comma, 562949953421312/556182861328125 = {{Monzo|49 -6 -17}}. The generator is ~512/375 = ~535¢. Seventeen generators equals a septuple-compound 5th.  5/4 is equated to 3 octaves minus 6 generators. An obvious 11-limit interpretation of the generator is 11/8, leading to the Lala-selo temperament. However, Lala-selo isn't nearly as accurate as Trisa-segu.
 ===[[Gammic family|Gammic or Laquinquadyo family]] (P8, P5/20)===
@@ Line 368: / Line 368: @@
 ===[[Hemifamity temperaments|Hemifamity or Saruyo temperaments]]===
 Hemifamity rank-two temperaments temper out the hemifamity comma, {{Monzo|10 -6 1 -1}} = 5120/5103.
+===[[Parkleiness temperaments|Parkleiness or Zotritrigu temperaments]]===
+Parkleiness rank-two temperaments temper out the ''parkleiness'' comma, {{Monzo|7 7 -9 1}} = 1959552/1953125.
 ===[[Porwell temperaments|Porwell or Sarurutrigu temperaments]]===